# Manchester Algebra Seminar - Alexis Langlois-Rémillard

Dates: | 31 January 2023 |
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Times: | 13:00 - 14:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, Current University students |

Speaker: Alexis Langlois-Rémillard - U Ghent

Title: Representations of the Dunkl total angular momentum algebra Abstract: The Dunkl total angular momentum algebra is the supercentraliser of the realisation of the orthosymplectic Lie superalgebra osp(1|2) present inside the tensor product of a rational Cherednik algebra and a Clifford algebra. Its representation theory changes according to the reflection group involved, the dimension of the space and a parameter function. In this talk, we focus on the four-dimensional case, with the group being the product of two dihedral groups. There we can define a subalgebra admitting a triangular decomposition that captures the structure of the finite-dimensional representations of the whole algebra. We then use it to give a coarse classification of the irreducible representations. We finish with some closing words sketching how to refine the coarse classification to a full classification.

Tea and biscuits 12:45 in the foyer